TSTP Solution File: SEV095^5 by Zipperpin---2.1.9999
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zipperpin---2.1.9999
% Problem : SEV095^5 : TPTP v8.1.2. Released v4.0.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bAYuKJJTLo true
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 19:59:35 EDT 2023
% Result : Theorem 88.41s 12.02s
% Output : Refutation 88.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 26
% Syntax : Number of formulae : 118 ( 1 unt; 15 typ; 0 def)
% Number of atoms : 1149 ( 2 equ; 203 cnn)
% Maximal formula atoms : 25 ( 11 avg)
% Number of connectives : 5767 ( 172 ~; 435 |; 38 &;4792 @)
% ( 0 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 16 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1168 (1168 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 15 usr; 6 con; 0-6 aty)
% ( 280 !!; 5 ??; 0 @@+; 0 @@-)
% Number of variables : 315 ( 14 ^; 285 !; 4 ?; 315 :)
% ( 12 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf('#sk9_type',type,
'#sk9': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf('#sk2_type',type,
'#sk2': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf('#form10_type',type,
'#form10': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $o ).
thf('#sk1_type',type,
'#sk1': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf('#sk4_type',type,
'#sk4': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf('#sk7_type',type,
'#sk7': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf('#sk5_type',type,
'#sk5': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf('#sk8_type',type,
'#sk8': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf('#sk6_type',type,
'#sk6': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i > $o ).
thf('#sk3_type',type,
'#sk3': ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > ( ( $i > $o ) > ( $i > $o ) > $i > $o ) > $i ).
thf(s_comb_type,type,
'#S':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > ( A > B ) > A > C ) ).
thf(c_comb_type,type,
'#C':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B > C ) > B > A > C ) ).
thf(b_comb_type,type,
'#B':
!>[A: $tType,B: $tType,C: $tType] : ( ( A > B ) > ( C > A ) > C > B ) ).
thf(k_comb_type,type,
'#K':
!>[A: $tType,B: $tType] : ( B > A > B ) ).
thf(i_comb_type,type,
'#I':
!>[A: $tType] : ( A > A ) ).
thf(cTHM122C_pme,conjecture,
? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [Xu: $i > $o,Xv: $i > $o] :
( ! [Xw_2: $i] :
( ( Xr_27 @ Xu @ Xv @ Xw_2 )
| ( Xr_28 @ Xu @ Xv @ Xw_2 ) )
=> ! [Xz: $i] :
( ( Xu @ Xz )
=> ( Xv @ Xz ) ) )
& ! [Xx: $i > $o,Xw_2: $i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
& ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ! [Xw_2: $i] :
( ( Xr_27 @ Xy @ Xz @ Xw_2 )
| ( Xr_28 @ Xy @ Xz @ Xw_2 ) )
& ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xy @ Xw_2 )
| ( Xr_28 @ Xx @ Xy @ Xw_2 ) ) )
=> ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xz @ Xw_2 )
| ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ) ).
thf(zf_stmt_0,negated_conjecture,
~ ? [Xr_28: ( $i > $o ) > ( $i > $o ) > $i > $o,Xr_27: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ! [Xu: $i > $o,Xv: $i > $o] :
( ! [Xw_2: $i] :
( ( Xr_27 @ Xu @ Xv @ Xw_2 )
| ( Xr_28 @ Xu @ Xv @ Xw_2 ) )
=> ! [Xz: $i] :
( ( Xu @ Xz )
=> ( Xv @ Xz ) ) )
& ! [Xx: $i > $o,Xw_2: $i] :
( ( Xr_27 @ Xx @ Xx @ Xw_2 )
| ( Xr_28 @ Xx @ Xx @ Xw_2 ) )
& ! [Xx: $i > $o,Xy: $i > $o,Xz: $i > $o] :
( ( ! [Xw_2: $i] :
( ( Xr_27 @ Xy @ Xz @ Xw_2 )
| ( Xr_28 @ Xy @ Xz @ Xw_2 ) )
& ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xy @ Xw_2 )
| ( Xr_28 @ Xx @ Xy @ Xw_2 ) ) )
=> ! [Xw_2: $i] :
( ( Xr_27 @ Xx @ Xz @ Xw_2 )
| ( Xr_28 @ Xx @ Xz @ Xw_2 ) ) ) ),
inference('cnf.neg',[status(esa)],[cTHM122C_pme]) ).
thf(zip_derived_cl0,plain,
~ ( ??
@ ^ [Y0: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ??
@ ^ [Y1: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !!
@ ^ [Y2: $i > $o] :
( !!
@ ^ [Y3: $i > $o] :
( ( !!
@ ^ [Y4: $i] :
( ( Y1 @ Y2 @ Y3 @ Y4 )
| ( Y0 @ Y2 @ Y3 @ Y4 ) ) )
=> ( !!
@ ^ [Y4: $i] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) ) ) )
& ( !!
@ ^ [Y2: $i > $o] :
( !!
@ ^ [Y3: $i] :
( ( Y1 @ Y2 @ Y2 @ Y3 )
| ( Y0 @ Y2 @ Y2 @ Y3 ) ) ) )
& ( !!
@ ^ [Y2: $i > $o] :
( !!
@ ^ [Y3: $i > $o] :
( !!
@ ^ [Y4: $i > $o] :
( ( ( !!
@ ^ [Y5: $i] :
( ( Y1 @ Y3 @ Y4 @ Y5 )
| ( Y0 @ Y3 @ Y4 @ Y5 ) ) )
& ( !!
@ ^ [Y5: $i] :
( ( Y1 @ Y2 @ Y3 @ Y5 )
| ( Y0 @ Y2 @ Y3 @ Y5 ) ) ) )
=> ( !!
@ ^ [Y5: $i] :
( ( Y1 @ Y2 @ Y4 @ Y5 )
| ( Y0 @ Y2 @ Y4 @ Y5 ) ) ) ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[zf_stmt_0]) ).
thf(zip_derived_cl1,plain,
~ ( ?? @ ( '#B' @ ?? @ ( '#S' @ ( '#B' @ '#S' @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#C' @ '#S' @ '#I' ) ) ) ) ) @ ( '#C' @ '#S' @ '#I' ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#B' ) @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#C' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(lams2combs,[status(thm)],[zip_derived_cl0]) ).
thf(zip_derived_cl2,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o] :
~ ( ?? @ ( '#S' @ ( '#S' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ ( '#C' @ '#S' @ '#I' ) ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ) @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) ) @ ( '#S' @ ( '#B' @ '#B' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#C' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (&) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ !! ) ) @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ '#S' ) ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) ) ) ) ) @ X2 ) ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl1]) ).
thf(zip_derived_cl3,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
~ ( ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) )
& ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
& ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl2]) ).
thf(zip_derived_cl4,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#B' @ '#S' @ ( '#B' @ (=>) ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl3]) ).
thf(zip_derived_cl5,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk1' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk1' @ X2 @ X4 ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#sk1' @ X2 @ X4 ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl4]) ).
thf(zip_derived_cl6,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) )
=> ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#sk1' @ X2 @ X4 ) ) @ ( '#sk2' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl5]) ).
thf(zip_derived_cl8,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#sk1' @ X2 @ X4 ) ) @ ( '#sk2' @ X2 @ X4 ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl10,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
=> ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl8]) ).
thf(zip_derived_cl13,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl16,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl13]) ).
thf(zip_derived_cl19,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) @ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl16]) ).
thf(zip_derived_cl22,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
& ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
=> ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl19]) ).
thf(zip_derived_cl28,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl37,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl28]) ).
thf(zip_derived_cl49,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl37]) ).
thf(zip_derived_cl61,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl49]) ).
thf(zip_derived_cl73,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl61]) ).
thf(zip_derived_cl7,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl6]) ).
thf(zip_derived_cl9,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl7]) ).
thf(zip_derived_cl11,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl9]) ).
thf(zip_derived_cl14,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl11]) ).
thf(zip_derived_cl17,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) @ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl14]) ).
thf(zip_derived_cl20,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
& ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
=> ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl17]) ).
thf(zip_derived_cl24,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl31,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl24]) ).
thf(zip_derived_cl40,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl52,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl40]) ).
thf(zip_derived_cl64,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ~ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl52]) ).
thf(zip_derived_cl76,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl88,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( '#form10' @ X2 @ X4 )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl73,zip_derived_cl76]) ).
thf(zip_derived_cl27,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
& ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl22]) ).
thf(zip_derived_cl35,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl46,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl35]) ).
thf(zip_derived_cl58,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl46]) ).
thf(zip_derived_cl70,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl58]) ).
thf(zip_derived_cl85,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl70]) ).
thf(zip_derived_cl76_001,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl93,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( '#form10' @ X2 @ X4 )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
inference(renaming,[status(thm)],[zip_derived_cl85,zip_derived_cl76]) ).
thf(zip_derived_cl12,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (=>) ) ) @ ( '#B' @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl10]) ).
thf(zip_derived_cl15,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#B' @ !! @ ( '#C' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (=>) ) @ ( '#S' @ ( '#B' @ '#C' @ ( '#B' @ ( '#B' @ (&) ) @ ( '#B' @ ( '#B' @ !! ) @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ '#S' ) @ ( '#B' @ ( '#B' @ ( '#B' @ (|) ) ) @ X4 ) ) ) @ X2 ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl12]) ).
thf(zip_derived_cl18,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (=>) @ ( '#C' @ ( '#B' @ (&) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) @ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) ) ) @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl15]) ).
thf(zip_derived_cl21,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
& ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
=> ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl18]) ).
thf(zip_derived_cl26,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl34,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl26]) ).
thf(zip_derived_cl45,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl34]) ).
thf(zip_derived_cl57,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl45]) ).
thf(zip_derived_cl69,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl57]) ).
thf(zip_derived_cl76_002,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl84,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( '#form10' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl69,zip_derived_cl76]) ).
thf(zip_derived_cl25,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
& ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl21]) ).
thf(zip_derived_cl32,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl42,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl32]) ).
thf(zip_derived_cl54,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl42]) ).
thf(zip_derived_cl66,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl54]) ).
thf(zip_derived_cl81,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl66]) ).
thf(zip_derived_cl76_003,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl91,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( '#form10' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X6 ) ),
inference(renaming,[status(thm)],[zip_derived_cl81,zip_derived_cl76]) ).
thf(zip_derived_cl36,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl27]) ).
thf(zip_derived_cl47,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl36]) ).
thf(zip_derived_cl59,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl47]) ).
thf(zip_derived_cl71,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl59]) ).
thf(zip_derived_cl86,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl71]) ).
thf(zip_derived_cl76_004,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl94,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( '#form10' @ X2 @ X4 )
| ~ ( '#sk2' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
inference(renaming,[status(thm)],[zip_derived_cl86,zip_derived_cl76]) ).
thf(zip_derived_cl33,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl25]) ).
thf(zip_derived_cl43,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl33]) ).
thf(zip_derived_cl55,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl43]) ).
thf(zip_derived_cl67,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl55]) ).
thf(zip_derived_cl82,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl67]) ).
thf(zip_derived_cl76_005,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl92,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( '#form10' @ X2 @ X4 )
| ( '#sk1' @ X2 @ X4 @ ( '#sk3' @ X2 @ X4 ) )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X6 ) ),
inference(renaming,[status(thm)],[zip_derived_cl82,zip_derived_cl76]) ).
thf(zip_derived_cl41,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl31]) ).
thf(zip_derived_cl53,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl41]) ).
thf(zip_derived_cl65,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl53]) ).
thf(zip_derived_cl76_006,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl80,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ~ ( '#form10' @ X2 @ X4 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ ( '#sk7' @ X2 @ X4 ) ) ),
inference(renaming,[status(thm)],[zip_derived_cl65,zip_derived_cl76]) ).
thf(zip_derived_cl76_007,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl78,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( '#form10' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl324,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: ( $i > $o ) > ( $i > $o ) > $i > $o,X2: $i] :
( ~ ( X1 @ ( '#sk4' @ X1 @ X0 ) @ ( '#sk6' @ X1 @ X0 ) @ ( '#sk7' @ X1 @ X0 ) )
| ( X0 @ ( '#sk1' @ X1 @ X0 ) @ ( '#sk2' @ X1 @ X0 ) @ X2 )
| ( X1 @ ( '#sk1' @ X1 @ X0 ) @ ( '#sk2' @ X1 @ X0 ) @ X2 )
| ~ ( X1 @ ( '#sk8' @ X1 @ X0 ) @ ( '#sk8' @ X1 @ X0 ) @ ( '#sk9' @ X1 @ X0 ) ) ),
inference('sup+',[status(thm)],[zip_derived_cl80,zip_derived_cl78]) ).
thf(zip_derived_cl23,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
& ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_imply,[status(thm)],[zip_derived_cl20]) ).
thf(zip_derived_cl29,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl38,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl29]) ).
thf(zip_derived_cl50,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl38]) ).
thf(zip_derived_cl62,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl50]) ).
thf(zip_derived_cl74,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl62]) ).
thf(zip_derived_cl76_008,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl89,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ~ ( '#form10' @ X2 @ X4 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 )
| ( X4 @ ( '#sk5' @ X2 @ X4 ) @ ( '#sk6' @ X2 @ X4 ) @ X8 ) ),
inference(renaming,[status(thm)],[zip_derived_cl74,zip_derived_cl76]) ).
thf(zip_derived_cl671,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
( ( ( X0 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
!= ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 ) )
| ( X2 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
| ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ~ ( '#form10' @ X2 @ X0 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl89]) ).
thf(zip_derived_cl735,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
( ( X0 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
| ( X2 @ ( '#sk5' @ X2 @ X0 ) @ ( '#sk6' @ X2 @ X0 ) @ X1 )
| ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ~ ( '#form10' @ X2 @ X0 ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl671]) ).
thf(zip_derived_cl78_009,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ~ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( '#form10' @ X2 @ X4 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl76]) ).
thf(zip_derived_cl30,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i] :
( ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) ) ) )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_and,[status(thm)],[zip_derived_cl23]) ).
thf(zip_derived_cl39,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) ) ),
inference(lazy_cnf_forall,[status(thm)],[zip_derived_cl30]) ).
thf(zip_derived_cl51,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ~ ( !! @ ( '#B' @ !! @ ( '#S' @ ( '#B' @ '#S' @ ( '#B' @ ( '#B' @ (|) ) @ ( '#S' @ X4 @ '#I' ) ) ) @ ( '#S' @ X2 @ '#I' ) ) ) )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_or,[status(thm)],[zip_derived_cl39]) ).
thf(zip_derived_cl63,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ~ ( !! @ ( '#S' @ ( '#B' @ (|) @ ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) @ ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) ) ) )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl51]) ).
thf(zip_derived_cl75,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 ) ),
inference(lazy_cnf_exists,[status(thm)],[zip_derived_cl63]) ).
thf(zip_derived_cl76_010,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o] :
( ( '#form10' @ X2 @ X4 )
| ~ ( ( X4 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) )
| ( X2 @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk8' @ X2 @ X4 ) @ ( '#sk9' @ X2 @ X4 ) ) ) ),
define([status(thm)]) ).
thf(zip_derived_cl90,plain,
! [X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X4: ( $i > $o ) > ( $i > $o ) > $i > $o,X6: $i,X8: $i] :
( ~ ( '#form10' @ X2 @ X4 )
| ( X4 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk1' @ X2 @ X4 ) @ ( '#sk2' @ X2 @ X4 ) @ X6 )
| ( X2 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 )
| ( X4 @ ( '#sk4' @ X2 @ X4 ) @ ( '#sk5' @ X2 @ X4 ) @ X8 ) ),
inference(renaming,[status(thm)],[zip_derived_cl75,zip_derived_cl76]) ).
thf(zip_derived_cl1107,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
( ( ( X0 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
!= ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 ) )
| ( X2 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
| ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ~ ( '#form10' @ X2 @ X0 ) ),
inference(eq_fact,[status(thm)],[zip_derived_cl90]) ).
thf(zip_derived_cl1171,plain,
! [X0: ( $i > $o ) > ( $i > $o ) > $i > $o,X1: $i,X2: ( $i > $o ) > ( $i > $o ) > $i > $o,X3: $i] :
( ( X0 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
| ( X2 @ ( '#sk4' @ X2 @ X0 ) @ ( '#sk5' @ X2 @ X0 ) @ X1 )
| ( X2 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ( X0 @ ( '#sk1' @ X2 @ X0 ) @ ( '#sk2' @ X2 @ X0 ) @ X3 )
| ~ ( '#form10' @ X2 @ X0 ) ),
inference(local_rewriting,[status(thm)],[zip_derived_cl1107]) ).
thf(zip_derived_cl4942,plain,
$false,
inference(eprover,[status(thm)],[zip_derived_cl88,zip_derived_cl93,zip_derived_cl84,zip_derived_cl91,zip_derived_cl94,zip_derived_cl92,zip_derived_cl324,zip_derived_cl735,zip_derived_cl78,zip_derived_cl1171]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SEV095^5 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.bAYuKJJTLo true
% 0.13/0.34 % Computer : n028.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 04:04:19 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Running portfolio for 300 s
% 0.13/0.35 % File : /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.35 % Number of cores: 8
% 0.21/0.35 % Python version: Python 3.6.8
% 0.21/0.35 % Running in HO mode
% 0.21/0.66 % Total configuration time : 828
% 0.21/0.66 % Estimated wc time : 1656
% 0.21/0.66 % Estimated cpu time (8 cpus) : 207.0
% 0.21/0.72 % /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
% 0.21/0.76 % /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.21/0.77 % /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
% 88.41/12.02 % Solved by lams/40_b.comb.sh.
% 88.41/12.02 % done 187 iterations in 11.161s
% 88.41/12.02 % SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
% 88.41/12.02 % SZS output start Refutation
% See solution above
% 88.41/12.02
% 88.41/12.02
% 88.41/12.02 % /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
% 88.41/12.02 % Terminating...
% 89.09/12.16 % Runner terminated.
% 89.12/12.18 % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------